<SEC-DOCUMENT>0001179110-21-006837.txt : 20210617
<SEC-HEADER>0001179110-21-006837.hdr.sgml : 20210617
<ACCEPTANCE-DATETIME>20210617183107
ACCESSION NUMBER:		0001179110-21-006837
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20210615
FILED AS OF DATE:		20210617
DATE AS OF CHANGE:		20210617

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Perestroika
		CENTRAL INDEX KEY:			0001729635
		STATE OF INCORPORATION:			V8
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-38373
		FILM NUMBER:		211026322

	BUSINESS ADDRESS:	
		STREET 1:		TRANSOCEAN LTD, TURMSTRASSE 30
		CITY:			STEINHAUSEN
		STATE:			V8
		ZIP:			6312
		BUSINESS PHONE:		0041417490500

	MAIL ADDRESS:	
		STREET 1:		TRANSOCEAN LTD, TURMSTRASSE 30
		CITY:			STEINHAUSEN
		STATE:			V8
		ZIP:			6312

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Transocean Ltd.
		CENTRAL INDEX KEY:			0001451505
		STANDARD INDUSTRIAL CLASSIFICATION:	DRILLING OIL & GAS WELLS [1381]
		IRS NUMBER:				980599916
		STATE OF INCORPORATION:			V8
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		TURMSTRASSE 30
		CITY:			STEINHAUSEN
		STATE:			V8
		ZIP:			6312
		BUSINESS PHONE:		41 41 749 0500

	MAIL ADDRESS:	
		STREET 1:		TURMSTRASSE 30
		CITY:			STEINHAUSEN
		STATE:			V8
		ZIP:			6312
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>edgar.xml
<DESCRIPTION>FORM 4 -
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-06-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001451505</issuerCik>
        <issuerName>Transocean Ltd.</issuerName>
        <issuerTradingSymbol>RIG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001729635</rptOwnerCik>
            <rptOwnerName>Perestroika</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>TURMSTRASSE 30</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>STEINHAUSEN</rptOwnerCity>
            <rptOwnerState>V8</rptOwnerState>
            <rptOwnerZipCode>6312</rptOwnerZipCode>
            <rptOwnerStateDescription>SWITZERLAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Registered Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2021-06-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3000000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4.17</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>70740354</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Registered Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2021-06-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2000000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>4.20</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>72740354</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F3"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $4.02 to $4.255, inclusive. The reporting person undertakes to provide Transocean Ltd. (the &quot;Company&quot;), any security holder of the Company, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in footnotes (1) and (2) to this Form 4.</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $4.09 to $4.29, inclusive.</footnote>
        <footnote id="F3">These securities are held directly by Perestroika AS. Mr. Frederik Mohn is a sole director and owner of Perestroika AS and is the beneficial owner of all securities owned by Perestroika AS.</footnote>
    </footnotes>

    <remarks>Perestroika (Cyprus) Ltd. is a wholly owned subsidiary of Perestroika AS. Due to Perestroika (Cyprus) Ltd.'s designation of a member of the board of directors of the Company, each of Perestroika (Cyprus) Ltd. and Perestroika AS, as its sole owner, may be deemed to be a director of the Company by deputization.</remarks>

    <ownerSignature>
        <signatureName>Daniel Ro-Trock By Power of Attorney</signatureName>
        <signatureDate>2021-06-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
